Tradeoffs among Free-flow Speed, Capacity, Cost, and Environmental Footprint in Highway Design

Chen Feng Ng and Kenneth A. Small

August 28, 2008

Abstract This paper investigates differentiated design standards as a source of capacity additions that are more affordable and have smaller aesthetic and environmental impacts than expressways. We consider several tradeoffs, including narrow versus wide lanes and shoulders on an expressway of a given total width, and high-speed expressway versus lower-speed arterial. We quantify the situations in which off-peak traffic is sufficiently great to make it worthwhile to spend more on construction, or to give up some capacity, in order to provide very high off-peak speeds even if peak speeds are limited by congestion. We also consider the implications of differing accident rates. The results support expanding the range of highway designs that are considered when adding capacity to ameliorate urban road congestion. Keywords: highway design, capacity, free-flow speed, parkway Journal of Economic Literature codes: L91, R42 Contacts: Chen Feng Ng: Department of Economics, California State University at Long Beach; cng3@csulb.edu Kenneth Small: Department of Economics, University of California at Irvine; ksmall@uci.edu An earlier version was presented to Third Kuhmo-Nectar Conference, Amsterdam, July 2008.

We are grateful to the University of California Transportation Center for financial support, and to many colleagues for comments on earlier drafts, especially Pablo Durango-Cohen, Robin Lindsey, Robert Noland, Robert Poole, Peter Samuel, Ian Savage, and Erik Verhoef. Of course, all responsibility for facts and opinions expressed in the paper lies with the authors.

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1. Introduction

Many analysts and policy makers have argued that building more highways is an

ineffective response to congestion: specifically, that it is infeasible to add enough highway

capacity in large urban areas to provide much relief. The argument is supported, for example, by

examining the funding requirements for a highway system that is estimated to accommodate

travel at acceptable levels of service. Such requirements come to hundreds of billions of dollars

for the entire US (US FHWA 2006b). This observation, along with impediments to various other

measures, has led Downs (2004) to conclude that there is little chance for a resolution to

congestion problems in the US.

Much of the expense envisioned in such lists of needs is for new or expanded expressway

routes.1 Expressways are very intensive in land and structures, requiring great expense and

disruption to existing land uses. Furthermore, the resulting road has significant environmental

spillovers on surrounding neighborhoods. These impacts, including air pollution, noise, and

visual impact, are closely related to the size of the road and even, in the case of noise and

nitrogen-oxide emissions, directly to speed itself. Thus there are significant tradeoffs that need to

be considered when deciding what kind of free-flow speed should be provided by a given

highway investment.

The highest-capacity roads built in the US are usually expressways, and they generally

conform to very high design standards. The most rigorous of these standards are those of the

federal Interstate system, which specify lane width, sight distance, grade, shoulders, and other

characteristics (AASHTO 2005). These standards are mainly dictated by two underlying

assumptions: the road must be safe for travel at high speeds (typically 55-70 mi/h in urban

settings), and it must be able to carry mixed traffic including large trucks.

But does it make sense to build high-speed roads that will be heavily congested for large

parts of the day, so that only a minority of vehicles experience those high speeds? And does it

make sense, in an area served by a grid of expressways, to design every major route to

accommodate large trucks?

1 See US FHWA (2006b), ch 7. Of the $84.5 billion in investments in urban arterial and collector roads meeting defined cost-benefit criteria in this report, 53 percent is for freeways and expressways – of which about half is for expansion, half for rehabilitation or environmental enhancement (Exhibit 7-3).

2

One way to look at the problem is in terms of equilibration of travel times. In a heavily

congested urban area, higher-quality roads become congested more severely than others, so that

levels of service tend to be equalized (Pigou 1920, Downs 1962). When this occurs, the extra

expense incurred to raise the design speeds on major roads has no payoff during congested

periods, whereas anything to improve capacity has a huge payoff. Clearly, then, one key factor

determining the ideal highway design will be the ratio of peak to off-peak traffic.

We can illustrate the tradeoffs by considering lane width. The standard 12-foot-wide

lanes of US interstate highways provide safety margins for mixed traffic at high speeds, often

under difficult conditions of weather and terrain. On most urban commuting corridors, there are

fewer trucks and speeds are low during much of the day; thus the need for such safety margins is

smaller. Indeed, urban expressway expansions are sometimes carried out by converting shoulders

to travel lanes and restriping all lanes to an 11-foot width. These have a disadvantage of slower

free-flow travel, and perhaps of higher accident rates – although as we shall see the evidence on

safety is mixed. The point here is that by squeezing lanes and shoulders, more capacity can be

obtained at the expense of some other desirable features. Hence, there is a tradeoff.

In this paper, we examine just a few of the tradeoffs involved by considering examples of

pairwise comparisons between two urban highway designs, in which as many factors as possible

are held constant. We first consider different lane and shoulder widths for a given highway type

(expressway or signalized arterial). In the case of the expressway, this really amounts to a

reconsideration of the “parkway” design that prevailed in the US prior to 1950, except we do not

attempt to account quantitatively for the truck restrictions, tighter curves, or nicer landscaping

that may further enhance this option. We then compare expressways with high-performance

unsignalized arterials. In each comparison, we characterize the range of conditions under which

the more modest design (narrower lanes, lower design speed) provides for greater travel-time

savings or involves the least total cost including user costs.

2. Congestion Formation, Capacity, and Travel Time

We consider four determinants of travel time on a highway. First is free-flow speed,

which for expressways is specified as a function of highway design including lane and shoulder

widths. Second is congestion delay due to the inflow of traffic at rates less than the highway’s

capacity; this is described by speed-flow curves. Third is further congestion delay due to queuing

3

when inflow exceeds capacity; this is described by a simple bottleneck queuing model. Fourth is

control delay, which applies only to arterials with signalized intersections. In this section, we

derive peak and off-peak travel times from basic relationships involving these four determinants.

In Section 3, we relate the parameters of these relationships numerically to highway design

parameters, and carry out the comparisons described earlier.

The first two determinants just described are summarized by a speed-flow function, S(V),

giving speed as a function of inflow. We define it for 0≤V≤VK, where VK is the highway’s

capacity defined as the highest sustainable steady flow rate.2 For expressways, speed decreases

as the flow rate approaches the expressway’s capacity. Figure 1 shows the speed-flow curves for

various free-flow speeds for expressways based on the 2000 edition of the Highway Capacity

Manual (Transportation Research Board 2000). The free-flow speed is S0≡S(0). For signalized

urban arterials, the speed-flow curve is flat, i.e., the speed on the urban street remains at the free-

flow speed for all flow rates up to the road’s capacity VK. This capacity is determined by the

saturation flow rate at intersections (the maximum flow rate while the signal is green) multiplied

by the proportion of the signal’s cycle time during which it is green.

2 Cassidy and Bertini (1999) suggest that the highest observed flow, which is larger, is not a suitable definition of capacity because it generally breaks down within a few minutes – although Cassidy and Rudjanakanoknad (2005) hold out some hope that this might eventually be overcome through sophisticated ramp metering strategies. Our speed-flow function does not include the backward-bending region, known as congested flow in the engineering literature and as hypercongested flow in the economics literature, because flow in that region leads to queuing which we incorporate separately. See Small and Verhoef (sect 3.3.1, 3.4.1) for further discussion of hypercongestion.

4

Figure 1. Speed-flow curves for different free-flow speeds for expressways

The third determinant, queuing delay, may be approximated by deterministic queuing of

zero length behind a bottleneck (Small and Verhoef 2007, sect 3.3.3). For the sake of

concreteness, we assume the bottleneck occurs at the entry to the section of road under

consideration.3 Suppose traffic wishing to enter the road arrives at rate Vo during an off-peak

period of total duration F, and at rate Vp during a peak period of duration P and starting at time

tp. We describe here the case Vo<VK<Vp so that a queue forms during the peak period and

vehicles leave the queue at the rate VK. We also assume F is long enough that the queue

disappears by the end of the off-peak period. The number of vehicles in the queue, N(t), builds

up at rate Vp-VK starting at time tp, causing queuing delay D(t)=N(t)/VK to a vehicle entering at

time t. At time tp′ = tp+P, the end of the peak period, this delay has reached its maximum value,

3 If the road is not of uniform capacity, the bottleneck would occur at the point of lowest capacity. This would require working out exactly how much flow occurs in each subsection in order to determine the non-queuing congestion delays, with only a small effect on the total travel times.

5

Dmax=P⋅[(Vp/VK)-1]. The queue then begins to dissipate, shortening at rate (VK-Vo) until it

disappears at time tx=tp′ +(Vp-VK)P/(VK-Vo).

The resulting queuing delay has the triangular pattern shown in Figure 2. The average

queuing delay to anyone entering during the peak period is

]1)/[(21

max21 −⋅== Kpp VVPDD . (1)

The same average queuing delay affects those arriving between times tp′ and tx, which when

averaged with the other off-peak travelers (who experience no queuing delay) produces the

average off-peak travel delay:

( )( )oKK

Kppo VVV

VVFP

FPxD

D−⋅

−⋅=

−⋅=

22

21

)( (2)

where x=tx-tp is the total duration of queuing (hence x-P=tx-tp′).

Figure 2. Queuing delay for vehicles arriving at road entrance at time t

In addition to queuing delay, urban arterial drivers face “control delay” reflecting time

lost slowing and waiting for signalized intersections — aside from the bottleneck queuing just

discussed. Let Z denote the number of signalized intersections on the urban street encountered on

a trip of length L. Based on the HCM’s procedure (see Appendix A), the average control delay

per vehicle for through movements, δ, is:

[ ])/)(/(1)/1(5.0 2

CgVVCgCZ

K−−⋅

⋅=δ (3a)

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where C is signal cycle length, g is effective green time, and V is the volume of traffic going

through the intersection. Time durations C, g, and hence δ are all conventionally measured in

seconds. Equation (3a) assumes that vehicles arrive at a signal at a constant rate V, which results

in queuing if the signal is red, and it incorporates the way this queue dissipates when the signal

turns green.4 That dissipation depends on lane-specific saturation rates, which we are able to

relate to the overall capacity VK of the highway (see Appendix A). Recall that due to our

assumption that this same capacity limits upstream flow, V is equal to the queue discharge rate

VK during the time period tp to tx (i.e., when queuing occurs at the bottleneck). At all other times,

V is equal to the off-peak volume, Vo. Thus, for peak travelers and for those off-peak travelers

who experience queuing at the bottleneck, the control delay for each vehicle is:

)/1(5.0 CgCZp −⋅⋅=δ . (3b)

For all other off-peak travelers, the control delay is given by (3a) with V=Vo:

[ ])/)(/(1)/1(5.0 2

CgVVCgCZ

Koo −

−⋅⋅=δ (3c)

We now combine all four sources of delay and add them over vehicles. Peak travelers, of

whom there are VpP, experience speed S(VK) while moving. Adding control delay and queuing

delay yields total travel time in hours:

++⋅= p

p

Kpp D

VSLPVTT

3600)(δ

. (4)

Among off-peak travelers, a fraction x-P travel at speed S(VK) while moving, whereas a fraction

F-x+P travel at speed S(Vo). Again adding control and queuing delay, their total travel time is:

( )

+

++−+

+−⋅= o

o

o

p

Koo DF

VSLPxF

VSLPxVTT

3600)()(

3600)(δδ

. (5)

Total travel time and average travel time are, respectively:

oPall TTTTTT += (6)

op

allall

FVPVTTTT+

= (7)

4 The delay in equation (3a) is also known as uniform delay, as described in Appendix A. It is based on Webster’s delay formulation; see Rouphail et al (1996) for a review of this and other methods for estimating control delay.

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3. Comparisons between Designs with Equal Construction Cost

In this section, we make two comparisons of roads with “regular” and “narrow” designs,

one for expressways and one for signalized urban arterials (which we shall refer to

interchangeably as urban streets). In each case, we hold constant the total width of the roadway

so there is very little cost difference between the two roads in each comparison. We also hold

fixed the distance between the two halves of the road, so we need only consider one half,

carrying traffic in one direction.

We ignore the difference in cost due to converting part of the paved shoulders in the

“regular” design to vehicle-carrying pavements in the “narrow” design; since the largest

component of new construction cost is grading and structures, this difference should be minor.

We also ignore any differences in maintenance cost that may occur because vehicles on narrow

lanes are more likely to veer onto the shoulder or put weight on the edge of the pavement

(AASHTO 2004, p. 311).

This comparison enables us to focus on the two primary factors that distinguish these

designs from each other: travel time and safety. As we will see, the safety advantages or

disadvantages of “narrow” versus “regular” design are not entirely clear, in part because lower

speeds help compensate for narrower lanes and less margin for error at the shoulder. We

therefore assume in this section that the two designs have identical accident rates, and return to

the safety issue in Section 5. This enables us to focus solely on travel time.

The 2000 Highway Capacity Manual (henceforth HCM) provides methodologies for

determining road capacities, free-flow speeds, and indeed the entire speed-flow functions for

expressways (which are called “freeways” by the HCM) and urban streets with different

specifications. As described in detail in Appendix A, we use this information to determine the

values VK, S(VK), and S(Vo) appearing in equations (3)–(5).

Our first example is expressways. Expressway R (the “regular” design) has two 12 ft

lanes in one direction, a 6 ft left shoulder, and a 10 ft right shoulder, bringing its total one-

directional roadway to 40 feet (see Figure 3a). These are the minimum widths recommended for

“urban freeways” by AASHTO (2004) except we have added two feet to the left shoulder.

Expressway N (the “narrow” design) has three 10 ft lanes, a 2 ft left shoulder, and an 8 ft right

shoulder. As shown in Table 1, this road’s narrower lanes and shoulders lead to a lower free-flow

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speed and thus a lower capacity per lane compared to Expressway R; but its total capacity (VK) is

higher since it has more lanes.

For signalized urban arterials, we compare two high-type urban arterial streets, each with

the same number of signalized intersections and the same one-directional road width (38 ft).

Following the lane and median width recommendations by AAHSTO (2004), the “regular” urban

street (Urban Street R) has two 12 ft lanes in one direction for through movement, a 6 ft left

shoulder (which provides for a 12 ft median in terms of a two-directional road) and an 8 ft right

shoulder (see Figure 3b). At signalized intersections, the entire median (consisting of the left

shoulders of both directional roadways) is used for a 12 ft exclusive left-turn lane (which

therefore occupies the same linear space as the left-turn lane facing it in the opposite direction).

The rightmost through lane is a shared right-turn lane, and the right shoulder width remains at 8

ft. We assign this urban street a speed limit of 55 mi/h.

The “narrow” urban street (Urban Street N) has three 10 ft lanes in one direction for

through movement, a 2 ft left shoulder, and a 6 ft right shoulder.5 At signalized intersections, the

right shoulder width is reduced to 3 ft; the additional roadway plus the median are used to

provide for an exclusive left-turn lane of 10 ft while maintaining three 10 ft through lanes, one of

which is a shared right-turn lane.6 We give it a speed limit of 45 mi/h.

These assumptions enable us to derive free-flow speeds and intersection delays by

following procedures in the HCM, as detailed in Appendix A. Table 1 shows selected results.

The free-flow time advantage for a trip of L=10 miles is 0.77 minutes for the “regular” compared

to the “narrow” expressway; and it is 1.17 minutes for the “regular” compared to the “narrow”

arterial. Recall that each pairwise comparison is of two roads occupying the same width and

hence with nearly identical construction costs.

5 A wider right shoulder is given priority over the left shoulder in order to provide adequate space for stopped vehicles and minimize the impact of such incidents on other vehicles.

6 Note that for the urban streets in Figure 3b, the total two-directional roadway width at the intersection itself is less than the sum of those of the two separate one-directional roadways, because the left turn lanes in both directions share the same linear space. That is, the width of the two directional roadways includes only the width of one, not two, left turn lanes. For the “regular” design this is 2x(12+12+8)+12 = 76 = 2x38, whereas for the “narrow” design it is 2x(10+10+10+3)+10 = 76 = 2x38; hence both are described as having a 38-foot one-directional roadway.

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Figure 3a. Example expressways (one direction)

Figure 3b. Example urban streets (one direction)

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Table 1. Specifications for examples (all one direction)

Freeway R: regular lanes & shoulders

Freeway N: narrow lanes & shoulders

Urban St R: regular lanes & shoulders

Urban St N: narrow lanes & shoulders

Parameters Number of lanes 2 3 2 3 Lane width (ft) 12 10 12 10 Left shoulder width (ft) 6 2 6 2 Right shoulder width (ft) 10 8 8 6 Total roadway (ft) 40 40 38 38 Length (mi) 10 10 10 10 Percentage of heavy vehicles1 0.05 0.05 0.05 0.05 Driver population factor1 1.00 1.00 1.00 1.00 Peak hour factor1 0.92 0.92 0.92 0.92 Interchanges/signals per mile1 0.50 0.50 0.50 0.50 Signal cycle length (s)1 - - 100 100 Effective green time (s)1 - - 70 70 Speed and capacity Free-flow speed (mi/h)2 65.5 60.4 51.5 46.8 Speed at capacity (mi/h)2 52.0 51.2 51.5 46.8 Capacity per lane (veh/h/ln)3 2,113.76 2,067.98 1,165.33 1,087.64 Total capacity, VK (veh/h)3 4,227.51 6,203.94 2,490.96 3,486.86 Travel time Free-flow travel time (min) 9.16 9.93 12.03 13.20 Notes: 1 In most cases, the default values recommended by the HCM are used; see Appendix A. The recommended default value for interchanges per mile is used for expressways, and we assume a comparable number for signal density on urban streets. The signal cycle length is based on the HCM’s default value for non-CBD areas (see Exhibit 10-16 of the HCM). A relatively high effective green time is chosen. 2 For expressways, the HCM calculates the average passenger-car speed based on total flow rate using passenger-car equivalents (pces) for heavy vehicles (a car has 1 pce). Our calculations are based on the average speed of passenger cars. 3 For urban streets, “capacity per lane” is based on the capacity of lanes which allow only through movement. See Appendix A for how total capacity is calculated for both expressways and urban streets.

Using the specifications listed in Table 1 and assuming duration of peak and off-peak

periods P=4 hours and F=12 hours, average travel times (which include queuing delay and

control delay, if applicable) can be calculated for a range of traffic volumes. Figures 4a-b show

the average travel times for the four different road designs under different values for average

daily traffic (ADT) and the ratio of peak volume (Vp) to off-peak volume (Vo). We see from

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Figure 4a that when Vp/Vo = 1.5, the “regular” freeway experiences queuing when ADT exceeds

50,724 veh/h, but queuing does not occur on the “narrow” freeway for ADT values up to 60,000

veh/h because the latter has a higher capacity. Once queuing begins, the increase in average

travel time is so marked that the average travel time on the “regular” freeway begins to exceed

that of the “narrow” freeway when ADT is just a little higher than the value at which queuing

begins. Some of this travel-time increase can be attributed to the lower speed when the lanes

become more crowded, but most of it is due to queuing delay. In the case of the signalized urban

arterials, the “regular” and “narrow” urban streets experience queuing when ADT exceeds

29,891 veh/h and 41,842 veh/h, respectively. The average travel time on the “regular” urban

street starts to exceed that of the “narrow” urban street when ADT is greater than 30,536 veh/h.7

Figure 4b shows the average travel times for the four highway types when Vp/Vo = 4.

With much higher traffic volumes during the peak hour compared to the previous scenario,

queuing now begins at lower values of ADT. Once queuing begins, average travel time on the

“narrow” design increases at a lower rate compared to the “regular” design because the former

has more capacity and thus discharges vehicles from the queue at a higher rate.

Thus even though the “regular” roads have slightly shorter average travel times

(compared to the “narrow” roads) when traffic volumes are low, this advantage is quickly erased

when they experience queuing — all the more so when Vp/Vo is large, since then more vehicles

experience queuing, the duration of the queue is longer, and fewer vehicles reap the advantages

of higher free-flow speed.

We can also calculate the values of ADT and Vp/Vo for which the difference in average

travel time between the “regular” and “narrow” designs is zero. Figures 5a-b show this (and

other) contour lines for freeways and urban streets, respectively — plotted so that a positive

number favors the “narrow” design. In both figures, the “narrow” design has shorter average

travel times compared to the “regular” design in the region to the right of the “0” contour line.

For the example freeways, the lowest value for the difference in average travel time (i.e. the

largest possible advantage for the regular design) is -0.77 minutes, which occurs under free-flow

conditions for both freeways. For the urban streets, the lowest difference is -1.17 minutes.

7 In Figures 4a and b, travel times for the “regular” and “narrow” urban streets are shown for ADT values up to 39,855 veh/h and 55,789 veh/h respectively because beyond that, the duration of the queue (x) exceeds the analysis period (F + P).

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Figure 4a. Average travel times for Vp/Vo = 1.5

Figure 4b. Average travel times for Vp/Vo = 4

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Figure 5a. Contour map of the difference in average travel time (“regular” expressway minus “narrow” expressway)

Figure 5b. Contour map of the difference in average travel time (“regular” urban street minus “narrow” urban street)

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We observe that the “narrow” design is strongly favored under all conditions in which

there is appreciable queuing. Most strikingly, the advantage of the “narrow” design increases

extremely rapidly with traffic. By contrast, the advantage of the “regular” design for light traffic

volumes is very modest and increases very slowly as traffic decreases. This is because the

“narrow” design’s advantage depends on queuing, whereas the “regular” design’s advantage

depends on the difference in free-flow speeds, which is quite small. While the specific numbers

depend on our particular examples, these broad features result from well-established properties

of highway design, and so are quite general.

4. Comparison between Expressways and Arterials with Equal Capacities

As seen in the previous section, signalized urban arterials tend have to lower free-flow

speeds and capacities than expressways. However, arterials also tend to have lower construction

costs. Thus it is useful to consider when it can be more cost-effective to build a lower-speed, less

expensive arterial instead of an expressway.

In order to make realistic comparisons, we now consider a very high type of arterial,

considerably higher than those of Section 3: namely, one that is divided, is uninterrupted by

traffic signals, and has driveway or side-street access no more than once every two miles. This

type of road is a type of “multilane highway” and differs from an expressway by allowing some

access by other than entrance and exit ramps; but it has grade-separated intersections for all

major crossings.8

We wish to examine total costs, including construction and travel-time costs, of a

network of expressways versus a network of unsignalized arterials, each with the same capacity.

We therefore compare the “regular” expressway from the previous section with an unsignalized

arterial with similar characteristics.9 Using the procedures outlined in Chapters 12 and 21 of the

HCM, this unsignalized arterial has a capacity of 3,945 veh/h — only seven percent less than that

8 According to the HCM (ch. 12-13), the most notable difference between a freeway and a multilane highway is that the former is characterized by full control of access. A “multilane highway” can have at-grade intersections and traffic signals with average spacing more than two miles.

9 We also considered a cost comparison between the “regular” expressway and the “regular” signalized urban street in the previous section. This comparison always favored the expressway because the urban street’s relatively low capacity (due to the presence of signalized intersections) means that 1.7 urban streets would have to be built in order to achieve the same capacity as the expressway. However, an expressway’s construction cost is only 1.3-1.5 times higher than that of an arterial, so the expressway is favored by both construction cost and travel-time cost.

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of “Freeway R” of Table 1. Its free-flow speed is 59.9 mi/h while average speed at capacity is

54.9 mi/h. This value for the arterial’s speed at capacity is slightly higher than that of the

expressway, due to the fact that speed falls less steeply with flow for unsignalized arterials than

for expressways (see Exhibits 21-3 and 23-2 of the HCM). While this situation might seem

artificial, it reflects what may well be a real advantage of the unsignalized arterial: more rapid

accelerations and decelerations on the expressway may introduce turbulence into its flow when

near capacity.

To equalize capacities, then, requires that the arterial network have 1.07 times the number

of lane-miles as the expressway network — implicitly assuming the network is large enough to

ignore indivisibilities. We therefore consider again a road section of L=10 miles, but multiply the

arterial construction cost by 1.07. We assume that roads in each network provide access to the

same origin and destination points, and that traffic volumes are distributed proportionally

throughout a given network so that average travel times for a ten-mile trip are the same

everywhere.

The free-flow travel time on the expressway is 9.16 minutes, compared to 10.02 minutes

for the unsignalized arterial network (difference: 0.86 minutes). At positive traffic volumes, the

expressway’s speed advantage erodes and eventually turns negative due to its steeper speed-flow

curve. Once capacity is reached (at the same travel volume, due to our equalizing capacities),

queuing sets in, with queuing delay identical for the two road networks.

Figure 6 shows the resulting contour lines of the difference in travel times (average travel

time on the expressway minus average travel time on the arterial network) for a range of Vp/Vo

and ADT values. The kinks seen in the -0.1 and -0.2 contour lines indicate the ADT at which

queuing begins for the corresponding Vp/Vo. For relatively low ADT (in the region to the left of

the “0” contour line), the expressway has shorter average travel times, but as just described it

loses this advantage eventually as ADT increases. Similarly, for a given ADT, the expressway’s

time advantage erodes and eventually is lost as Vp/Vo increases because then fewer travelers

benefit from its higher speed under light traffic conditions.

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Figure 6. Contour map of the difference in average travel time (expressway network minus unsignalized arterial network)

Thus, in the region to the right of the “0” contour line, building a network of unsignalized

arterials is more cost-effective than building an expressway network of the same capacity, since

the arterial has lower construction costs in addition to shorter travel times. However, when the

expressway has shorter average travel times, we need to weigh the annual travel time savings

against amortized construction costs. We examine this for the case where peak volume, Vp, is

equal to 1.05×VK, so that each road network experiences a small amount of queuing, We again

consider two values of Vp/Vo: 1.5 and 4. Under these conditions, average travel time on the

expressway is 0.37 minutes shorter than that on the arterial network for Vp/Vo = 1.5, and 0.05

minutes shorter for Vp/Vo = 4.

To calculate travel time savings, we multiply the difference in average travel time by the

ADT, by 250 days per year, and by an assumed value of travel time. We take the latter to be

$10.04 in our base case, with plus or minus 30% as low and high cases.10 The resulting aggregate

travel-time cost savings of the expressway versus the arterial network are shown in Table 2.

10 As suggested by Small and Verhoef (2007, sect. 2.6.5), the value of time is estimated as 50% of the wage rate. According to the US BLS (2007, Table 37), the mean hourly wage for civilian workers in metropolitan areas was $20.08 in 2006.

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Table 2. Travel-time cost savings for Vp = 1.05VK (in thousands of dollars/year)

Vp/Vo = 1.5 Vp/Vo = 4

Base value of time: $10.04 825 63 Low value of time: $7.03 577 44 High value of time: $13.05 1,072 82

We now turn to construction costs. Table 3 presents estimates of construction costs for

expressways and other principal arterials compiled by Alam and Kall (2005) for the US Federal

Highway Administration’s Highway Economic Requirements System (HERS) model, based on

samples of actual projects. These figures show that construction cost per additional lane on new

alignment is typically 23-31 percent lower for an arterial than for an expressway, with the larger

differences applying to larger urban areas. Here we restrict our consideration to urban areas of

more than 200,000 people.

Table 3. Construction costs per lane on new alignment in urban areas (thousands of 2007 $ per mile)1

Expressway Other Principal Arterial High-Type Arterial

Urban area population

(1000s) Total % ROW Total % ROW Total % ROW

200-1,000 15,392 3.0% 10,686 5.7% 13,039 4.1% >1,000 19,260 18.3% 14,717 18.3% 16,988 18.3%

Source: See text for last two columns. Other columns computed as follows. Roadway costs are from Alam and Kall (2005, Table 9). Non-roadway costs other than right of way (i.e., engineering, environmental impact and mitigation, intelligent transportation systems, urban traffic management, and bridges) are from multipliers for road way costs, in Alam and Kall (2005, Table 13). Right of way (ROW) costs are from Alam and Ye (2003, Table C-10) in the case of urban areas of 200-1,000 thousand, and from the multiplier 0.39 as recommended by Alam and Kall (2005, Table 13) in the case of urban areas of more than 1 million. All costs have been updated from 2002 to 2007 price levels using the US price deflator index of new one-family houses under construction (US Census Bureau 2008), which rose by 30.6% over those five years.

However, the cost differences from the HERS model are likely to overstate those

applying to our comparison for two reasons. First, we are considering a higher type of arterial

than the average in the sample. Second, these figures are based on averages for traffic conditions

prevailing on actual roads built, and so may overstate somewhat the differences that would occur

for a given (fixed) set of traffic conditions. Therefore we assume that the applicable costs for our

18

high-type arterial are midway between those for expressway and other principal arterials shown

in Table 3. The resulting costs are shown in the last column of the table.

Using the costs in Table 3, the amortized construction cost per lane-mile is calculated as

r·CROW +[r/(1 – e-rλ)]·Cother, where CROW and Cother are right-of-way and other construction costs,

r is the interest rate (assumed to be 7%), and λ is the effective lifetime of the road (assumed to be

20 years).11 This amortized cost is then multiplied by the number of lanes (2), the length of the

road (10 miles), and the relative number of roads (i.e., 1.00 expressway, 1.07 arterials) to obtain

the total amortized construction cost of the compared road sections. Table 4 shows the results for

six different cases governing the construction-cost differential between arterials and

expressways. The “base” cost differential reflects costs given in Table 3 (for the larger two sizes

of metropolitan areas). The “higher” and “lower” differentials are 1.5 and 0.5 times the base

differential.

Table 4. Difference in amortized construction costs for equal-capacity expressway and arterial networks (in thousands of 2007 dollars per year)

Urban area population (1000s)

Cost differential 200-1,000 >1,000 Base 2,725 1,920 Low (x0.5) 1,363 960 High (x1.5) 4,088 2,880

We can immediately see that unsignalized arterials are more cost-effective than

expressways under most scenarios here, because the difference in travel-time cost is relatively

small while the difference in construction cost is much higher. That is, nearly all the numbers in

Table 3 are smaller than any of the numbers in Table 4. There is only one exception: if we use

the high value of time, along with the low peak-to-off-peak ratio, then the travel-time saving of

the expressway is quite large, $1072 thousand per year; whereas if the construction-cost

differential is low and the area has population above 1 million, then the expressway’s cost

disadvantage is smaller than this, only $960 thousand. In all other cases shown, the higher cost of

11 The US Office of Management and Budget (US OMB 1992) recommends 7 percent as the real interest rate for cost-benefit analysis of transportation and other projects.

19

building the expressway more than offsets its travel-time advantage. Selected cases are shown in

Table 5.

Table 5. Construction and travel-time cost differential (expressway minus arterial), for Vp=1.05VK, urban population > 1 million, value of time = $10.04/h

($1000s/year)

Vp/Vo Construction Cost Differential 1.5 4.0 Low 135 897 Base 1,095 1,857 High 2,055 2,817

5. Safety

Conventional wisdom is that many of the smaller-footprint design features considered here –

narrow lanes, narrow shoulders, sharper curves, and so forth – would increase traffic accidents.

This belief underlies many of the recommended standards in AASHTO (2005). We consider in

this section whether increased accident costs would be likely to alter the results found so far.

Because accident costs are strongly dominated by injuries and fatalities (Small and Verhoef

2007, p. 100-103), we consider evidence on them rather than on all accidents. We also consider

only urban arterials or freeways of four or more lanes.

The conventional wisdom relies on several posited uses of extra lane or shoulder width:

more room to accommodate temporary inattention, more room to maneuver in case of a near-

accident, ability to make emergency stops off the main roadway. But there are compensating

behaviors that tend to offset these advantages: higher speeds, possibly closer vehicle spacing,

and a tendency to use wide shoulders for discretionary stops — which are dangerous because

many accidents are associated with a vehicle stopped on the shoulder.12 The speed increase is

especially well documented, with some evidence that it occurs unconsciously (Lewis-Evans and

Charlton 2006).

12 See for example Hauer (2000a, p. 1.1) and Hauer (2000b, p. 2.1). The latter source states that 10 percent of fatal freeway accidents are due to vehicles stopped in the shoulder, and that among such stopped vehicles discretionary stops outnumber emergency stops by a factor of 7 for cars and 5 for trucks.

20

Statistical studies of the safety effects of wider or straighter roads do not lead to any

consistent conclusion. This is partly because there are many unmeasured road attributes, such as

age and hazardous terrain, that are closely correlated with design features and so may confound

an attempt to isolate the effects of those design features. We review a few of the more

enlightening studies here.

Hadi et al. (1995, Table 2) find a statistically significant effect of lane width for just two

of the five types of urban multilane roads studied, with narrow lanes increasing fatal and injury

accidents. The same is true of paved shoulder width. In each case, the statistical models for the

other three road types omit the variable in question, either because of statistical insignificance or

unexpected sign: thus, we cannot tell whether there may be cases in which narrow lanes or

shoulders tend to reduce accidents.

Two studies have compared freeway segments before and after conversion from standard

to narrow lanes, sometimes with shoulder narrowing as well. Curren (1995, pp. 35-41) finds a

substantial and statistically significant increase in accident rates in three corridors studied; but a

decrease, albeit not statistically significant, in the other two corridors studied. The increases were

observed in those corridors in which both lanes and shoulders were quite narrow after

conversion. Bauer et al. (2004) find an average 10–11 percent increase in accident frequency in

before-and-after studies of urban freeway conversions from four to five lanes. A limitation of

this approach is that other aspects of road geometry are likely to have been changed at the same

time.

Potts et al. (2007) find generally inconsistent or statistically insignificant effects of lane

width in cross-sectional comparisons across urban and suburban arterial roads, both in Minnesota

(Minneapolis-St. Paul area) and Michigan (northern Detroit metropolitan area). Relative to a 12-

foot lane, they find a small increase in injury accidents for 11-foot lanes, and a bigger increase

for 10-foot lanes, in one out of four cases of multilane arterials in Minnesota; but inconsistent

effects, including several where narrower lanes reduced injury crashes, in Michigan (Tables 4

and 5). They conclude:

There was no indication that the use of … 10- or 11-ft lanes, rather than … 12-ft lanes, … led to increases in accident frequency [with the caveat that] one of the states analyzed [Minnesota] showed an increase in crash rates for four-lane undivided arterials with lane widths of … 10 ft or less. (p. 81)

21

The full study from which the results of Potts et al. are drawn also investigates shoulder width,

finding that wider shoulders do substantially reduce one important category of accidents: multi-

vehicle collisions not associated with intersections or driveways.13

Noland and Oh (2004) take a quite different approach, analyzing the aggregate number of

accidents in each of 102 counties in Illinois in year 2000, as a function of average road

characteristics in that county. They basically find no effects, although this may be because the

data are so highly aggregated.14 They offer as an explanation a version of Peltzman’s offsetting

behavior hypothesis (Peltzman 1975), by which safety improvements are partially or fully offset

by more aggressive driving. Noland and Oh also point out that most studies finding a negative

relationship between traffic accidents and conventional design elements (such as lane width)

include few if any controls for demographics. We should mention that analyzing offsetting

behavior is complex, because the various factors affecting drivers’ speed and aggressiveness

include some that affect how onerous or how pleasurable driving is (Steimetz 2008).

Milton and Mannering (1998) examine accident data from Washington State and find

some evidence that narrow lanes and shoulders increase accident frequencies at least in some

cases. These comparisons hold constant the posted speed limit but not the frequency of access

points, making it difficult to know whether the finding would still hold in comparing two roads

with different speed limits but identical numbers of access points. Similarly, Kweon and

Kockelman (2005, Table 3) find that narrower shoulders reduce fatal and injury crash rates, by

about 2.6 percent for every foot.

To summarize, both theoretical and empirical evidence linking road design to safety are

ambiguous, although on balance they contain some indications that greater lane width and

shoulder width may increase safety. Thus, we think it is an open question whether the “narrow”

road designs considered here would in fact reduce safety, but it is certainly a potential concern.

Probably it would depend on factors that vary from case to case, especially the speeds chosen by

drivers.

13 Harwood et al. (2007), ch. 5, especially Table 34. 14 One indication is that even population, the only scale variable included, has a very small and statistically insignificant effect (elasticity about 0.01–0.06), despite the logical expectation that number of accidents would depend in some way on number of vehicles being driven.

22

This suggests a strategy of accompanying such roads with lower speed limits and/or other

measures to discourage speeding. Of course, that raises the question of why not adopt such

measures in any case. It appears that governments live in an uneasy balance between taking

measures known to reduce injuries and fatalities, yet avoiding measures viewed by drivers as too

intrusive. Whatever the effects of road design taken by itself, the way road design might interact

with these other measures probably has a greater impact on safety. Our reading of the guidelines

on highway design suggest that speed-reducing measures are more likely to be accepted when

the road design is modest, because drivers then intuitively understand the rationale for them.

Therefore it seems quite likely that a strategy can be developed that includes lower-footprint road

designs as well as equal or better safety.

Several innovations in Europe offer hope that roads designed for lower speeds could be

accompanied by measures to ensure that lower speeds in fact prevail. Variable speed limits have

been used for many years in Germany and the Netherlands, and recently in Copenhagen,

primarily to smooth traffic during the onset of congestion — but also with a strong reduction in

injury accidents in one German implementation.15 Another approach, used occasionally in the

Netherlands and Denmark, is to is to enforce speeds by tracking vehicle licenses between control

points separated by a known distance. The most draconian approach is the installation of on-

vehicle systems that limit speed, with varying degrees of driver option to ignore or disable them.

On-road demonstration studies of such systems have been carried out in Sweden, the

Netherlands, Spain, and the UK (Liu and Tate 2004). The most effective speed limiters use

“intelligent speed adaptation” to vary the allowed speed with traffic conditions. Studies using

laboratory driving simulators and traffic simulation models have found that speed limiters are

likely to reduce average speed, speed variation, and lane-changing movements during

uncongested times — all of which are known to reduce accident rates — with little or no

detrimental effects on traffic flow during congested periods.16

Another potentially significant safety consideration is use of automobile-only roads. As

noted in the Introduction, such roads offer considerable savings in construction cost and use a

lower environmental footprint. Might they also alleviate negative safety impacts of more

environmentally friendly designs? Here again the evidence is mixed, but suggests that there 15 See Mirshahi et al. (2007), pp. 17-18, 24, 28-29. 16 See Compte (2000), Liu and Tate (2004), and Toledo, Albert, and Hakkert (2007).

23

probably would be such safety advantages. Lord, Middleton, and Whitacre (2005) find that on

the New Jersey Turnpike, which has two car-only and mixed-traffic roadways that are

approximately equivalent in other respects, accident rates are higher in the mixed-traffic roadway

and trucks are disproportionately involved in accidents there. Fridstrøm (1999) finds that overall

injury accident rates are nearly four times as responsive to amount of truck travel than to amount

of car travel. Countering this is a finding by Hiselius (2004) that truck travel reduces the number

of total accidents (injuries are not broken out separately); but this study is restricted to rural roads

(in Sweden). Overall, then, it seems likely that the kind of strategy investigated in this paper —

especially reducing lane widths — could be enhanced by combining it with more use of

automobile-only roads (perhaps supplemented by some truck-only roads). To investigate this

more fully would require additional analysis of traffic flow, construction and maintenance cost,

and accident rates in mixed traffic compared to homogeneous traffic.

Despite the empirical uncertainty about safety effects of road designs, it is useful to

assess the possible magnitudes of costs of increased accidents that could occur. Consider, then,

the finding of Bauer et al. (2004) that narrower lanes might increase accident rates by around 10

percent, and suppose this applies equally to fatality and injury accidents. This is almost identical

to the reductions found by Kweon and Kockelman (2005) for the four-foot shoulder reduction

that we consider in Section 3. Small and Verhoef (2007, pp. 100-103) estimate average social

costs of accidents for a US urban commuting trip at $0.14 per vehicle-mile. Thus a 10 percent

increase in accident rates would be an increase of $0.014 per vehicle-mile. Over a ten-mile road

section, this increased cost of $0.14 per vehicle would offset a travel-time savings of 0.84

minutes if value of time is $10 per hour (approximately the value used in the base scenario in the

previous section). This would reverse the advantage of the “narrow” design in only a very small

slice of the parameter space illustrated in Figure 5. Thus, it seems unlikely that safety

considerations would reverse any of the conclusions of our analysis in Section 3.

What about our comparison of expressways versus arterials in Section 4, which holds

lane width constant? Expressways are generally recognized to be safer than arterials, despite the

higher speeds and more difficult lane maneuvers often encountered on expressways. In 2006, the

fatality rate per 100 million vehicle-miles traveled on expressways was 0.62, compared to 1.13

for other principal arterials (US FHWA, 2006a). Kweon and Kockelman (2005) examine the

effects of functional category, speed limit, curvature, and other variables on accident rates in

24

Washington State. They find that expressways of Interstate standards are associated with a

46.1% and a 14.7% decrease in fatal and injury crash rates, respectively, compared to other

limited-access principal arterials.17 These effects could be modified if we accounted for the

higher speed limit of an expressway; we do not make such an adjustment because although speed

limit is controlled for in their model, it produces non-monotonic and somewhat unreliable results

according to their discussion — as indeed it does in several other studies, probably due to

confounding variables.18 However, we do adjust for the likelihood that our high-type arterial is

safer than an average arterial; consistent with our treatment of the cost differential, we assume its

safety disadvantage relative to an expressway is half that of an average arterial.

Using these results and Small and Verhoef’s (2007, Table 3.4) estimates that the social

costs per mile of fatal and injury accidents are $0.077 and $0.057, respectively, the social costs

for a ten-mile expressway section are lower by $0.18 and $0.04 per trip due to lower fatal and

injury accidents, respectively, compared to an arterial. Multiplying these costs by ADT and 250

days per year, the difference in the annual social costs of both types of accidents for the example

networks in Section 4 is about $2.9 million and $1.7 million for Vp/Vo = 1.5 and Vp/Vo = 4,

respectively. Comparing these differences with the values in Table 5, we find that the arterial

network has lower costs only in two of the six parameter values shown there: namely the base

and high cost differentials when Vp/Vo = 4. The numbers used here are imprecise, especially

since Kweon and Kockelman point out that there is not much variation in their data on fatal

accidents; but these numbers suggest that the relative safety features of expressways versus

arterials may be quite important in a cost-benefit analysis.

We conclude that accident costs potentially, although not certainly, offset the potential

advantage of an arterial compared to an expressway, given the current determinants of safety on

roads. Thus we believe that any move to replace expressways with arterials in metropolitan

17 These numbers are computed as the differences between the coefficients on “indicator for interstate highway” and “indicator for principal arterial” for the columns “fatal crash” and “injury crash,” respectively, in Kweon and Kockelman (2005, Table 3). Note the “indicator for limited access” applies to both roads so is not part of the comparison. 18The effect of speed limit in Kweon and Kockelman’s multi-equation model is complex and largely absent for fatality crashes; they consider it unreliable due to limited fatality observations and to correlation with unobserved design variables. In an auxiliary model, they find that observed increases in speed limits over the time period of their data decreases accidents up to a change to 60 mi/hr, then increases them. Other studies obtaining inconsistent or counter-intuitive results for speed include

25

planning would need to be accompanied by a thorough analysis of accidents and would best be

part of a comprehensive approach to using speed control or other measures to address safety.

6. Conclusion

It seems that the intuitive arguments made in the introduction hold up under quantitative

analysis. For both freeways and signalized urban arterials, squeezing more lanes into a fixed

roadway width has huge payoffs when highway capacity is exceeded by even a small amount

during peak periods, whereas the payoff from the higher off-peak speeds offered by wider lanes

and shoulders is very modest. The advantage of the road with narrower lanes is accentuated

when the ratio of peak to off-peak traffic is large. Similarly, for a wide range of parameters

governing construction costs and values of time, the savings in travel-time costs offered by a

network of expressways, compared to an equal-capacity network of high-type unsignalized

arterials, is considerably smaller than the amortized value of the extra construction costs

incurred. However, if accident costs are included, arterials may no longer have a cost advantage

in some scenarios since expressways are associated with substantially lower accident rates,

especially for fatal crashes.

Of course, the pairwise comparisons presented here do not come close to depicting the

full range of relevant alternatives for road design. And because so many properties of highways

are site-specific, results comparable to ours cannot be assumed to apply to any particular case

without more detailed calculations. Nevertheless, we think these results provide guidance as to

what types of designs deserve close analysis in specific cases, and they may provide guidance for

overall policy in terms of the type of road network to be planned for. We suspect that in many

cases such a network will have fewer expressways built to interstate standards, and more lower-

speed expressways and high-type arterials, than are now common in the US.

Current trends present a mixed picture as to how the relative advantages of different

highway designs are likely to change over time. Intractable congestion and general growth of

travel, along with limited capital budgets, seem to dictate increasing traffic but probably some

peak spreading, thus moving highway parameters toward the lower right in Figures 5 and 6, with

uncertain implications for the comparison. If congestion pricing became widespread, that would

curtail traffic while tending to make it more evenly distributed, thus moving parameters toward

the lower left and making current practice relatively more attractive.

26

Aside from the advantages quantified here, it seems likely that the more modest highway

designs suggested by these comparisons will also have more pleasing environmental and

aesthetic impacts. Highways with slower free-flow speeds can fit better into existing

geographical landforms and urban landscapes, permitting more curvature and grades and so

requiring less earth-moving and smaller structures such as bridges and retaining walls. Tire noise

and nitrogen oxides emissions are likely to be lower. Neighborhood disruption due to land

condemnation and construction should be less. These advantages depend on reductions in speeds

commensurate with the highway design, implying an important interaction between policies

toward highway design and those toward speed control.

27

Appendix A. Speeds and capacities from the HCM

This appendix discusses the HCM’s methodology for calculating speeds and capacities

for expressways, which the HCM calls “freeways” (based on HCM ch. 13, 23), and urban streets

(based on HCM, ch. 10, 15, 16). The procedure for unsignalized urban arterials (“multilane

highways” in the HCM’s terminology) is generally quite similar to that of expressways, with

slightly different parameter values in the speed/capacity equations (HCM ch. 12, 21).

A.1 Expressways/Freeways

Capacity varies by free-flow speed, and so the first step is to estimate free-flow speed.

The equation below is used to estimate free-flow speed (FFS) of a basic freeway segment (see

equation 23-1 in HCM):

FFS = BFFS – fLW – fLC – fN - fID (A.1)

where BFFS is the base free-flow speed (70 mi/h for urban freeways as stated in Exhibit 13-5 of

the HCM), fLW is the adjustment for lane width, fLC is the adjustment for right-shoulder lateral

clearance, fN is the adjustment for number of lanes, and fID is the adjustment for interchange

density. The tables for these adjustment factors can be found in Exhibits 23-4 to 23-7 in the

HCM, and are described below in relation to our example freeways in Section 3 of this paper.

The lane width adjustment, fLW, is 0 when lane width is 12 ft and 6.6 when lane width is

10 ft. The width of the left shoulder has no impact on free-flow speed, while there is no reduction

in free-flow speed when the right shoulder is wider than 6 ft. Thus, the right shoulder lateral

clearance adjustment, fLC, is 0 for the freeways in our example. The “regular” freeway in our

example has 2 lanes and the “narrow” freeway has 3 lanes, and so the adjustment for number of

lanes (fN) are 4.5 and 3.0 respectively. Assuming that there are 0.5 interchanges per mile as

recommended by the HCM gives us fID = 0.

The HCM states that base capacity is “2,400, 2,350, 2,300, and 2,250 pc/h/ln at free-flow

speeds of 70 and greater, 65, 60, and 55 mi/h, respectively” (p. 23-5). A simple formula can be

derived from this information, as shown in Appendix N of the Highway Performance Monitoring

System (HPMS) Field Manual (Federal Highway Administration, 2002):

≥<+

=70for 70for

400,210700,1

FFSFFSFFS

BaseCap (A.2)

where BaseCap is in passenger-cars per hour per lane.

28

The HCM also gives a formula (equation 23-2) for converting hourly volume V, which is

typically in vehicles per hour, to the equivalent passenger-car flow rate vp, which is in passenger-

car equivalents per hour per lane (pce/h/ln) and is used later on to estimate speed:

)/( pHVp ffNPHFVv ×××= (A.3)

where PHF is the peak-hour factor (which represents variation in traffic flow within an hour), N

is the number of lanes in one direction, fHV is the adjustment for heavy vehicles, and fp is the

adjustment for driver population (which indicates whether drivers consist of commuters who are

familiar with the road or recreational drivers). For the general case where there are no data

available, the HCM in Exhibit 13-5 recommends PHF = 0.92 for urban roads and fp = 1.00 (i.e.,

familiar drivers).

The HCM also recommends that in the general case, the percentage of heavy vehicles on

the road can be assumed to be 5% in urban settings (Exhibit 13-5). We assume that heavy

vehicles on the road consist only of trucks and buses (no recreational vehicles), and that the

expressway is on level terrain. This gives us fHV = 0.98 (based on equation 23-3 of the HCM).

Using equation A.3, we can convert BaseCap (which is in passenger-car equivalents per

hour per lane) to capacity in terms of vehicles per hour for all lanes, as shown in Appendix N of

the HPMS Field Manual. The HPMS Field Manual calls this PeakCap, and we refer to it as VK

in the model:

PeakCap = BaseCap × PHF × N × fHV × fp (A.4)

The HCM also has speed-flow diagrams which depict average passenger-car speed S

(mi/h) as a function of the flow rate vp (pce/h/ln). We consider free-flow speeds between 55 and

70 mi/h, in which case the following formulas apply (see Exhibit 23-3 in the HCM):

For vp ≤ (3,400 – 30FFS):

S = FFS (A.5a)

For (3,400 – 30FFS) < vp ≤ (1,700 + 10FFS):

( )

−−+

−−=6.2

700,140400,330

)340791

FFSFFSv

FFSFFSS p (A.5b)

29

A.2 Urban arterials

The HCM groups urban arterial streets into several design categories. We focus on high-

speed principal arterials (design category 1), which have speed limits of 45-55 mi/h and a default

free-flow speed of 50 mi/h (Transportation Research Board 2000, Exhibits 10-4 and 10-5). The

HCM provides little guidance for estimating free-flow speeds when field measurements are not

available, and so we use the procedure recommended by Zegeer et al (2008, pp. 66-73). We take

the case with no curbs or driveway access points along the road. Free-flow speed is then equal to

a “speed constant” which in turn depends on the speed limit of the road. We assume the speed

limits on the “regular” and “narrow” arterials are 55 mi/h and 45 mi/h respectively, which gives

us free-flow speeds of 51.5 mi/h and 46.8 mi/h.

A vehicle’s travel time on an urban street (ignoring queuing due to volumes exceeding

capacity, computed separately in the text) consists of running time plus “control delay” at a

signalized intersection. Based on Exhibit 15-3 of the HCM, running time for an urban arterial

longer than one mile is calculated as simply the length divided by the free-flow speed; that is, the

speed-flow curve is flat.

Control delay is the additional delay caused at intersections by stopping and/or waiting

behind other stopped vehicles while they start up and proceed through the intersection. The

HCM considers separately each “lane group” consisting of through lanes, exclusive left-turn

lanes, or shared turn/through lanes. It also states that “[t]he control delay for the through

movement is the appropriate delay to use in an urban street evaluation” (p. 15-4). With this, we

will focus on only two lane groups, through lanes and shared right-turn/through lanes, because a

given trip would make at most one left turn and we are not concerned with the time that requires.

The formula for calculating control delay for each lane group (equation 16-9 in the HCM)

is the sum of three components: (1) uniform control delay, which assumes uniform arrivals; (2)

incremental delay, which takes into account random arrivals and oversaturated conditions

(volume exceeding capacity); and (3) initial queue delay, which considers the additional time

required to clear an existing initial queue left over from the previous green period. As described

in Section 2, our model assumes that queuing due to oversaturation occurs at the entry to the

road, and that the queue discharges at a rate equal to the capacity of the road. Thus the traffic

volume arriving at the intersection is never greater than the intersection’s capacity, so only the

30

uniform control delay is applicable. (Capacity is calculated based on an intersection’s through

movement capacity, as detailed below.)

The control delay is then calculated for each lane group using equations 16-9 and 16-11

of the HCM:

[ ] PFCgX

CgCd ⋅−

−=

)/)(,1min(1)/1(5.0 2

(A.6)

where C is the cycle length, g is effective green time, X is the volume-to-capacity ratio of that

lane group, and PF is a “progression adjustment factor” which accounts for the effects of

synchronization (or lack of it) between adjacent signals. Using the defaults recommended by the

HCM for signals spaced 3,200 or more feet apart (denoted as Arrival Type 3, see p. 10-23 of the

HCM), we have PF = 1. We assume that the through lane group and the shared right-

turn/through lane group have identical values of g/C and that traffic distributes across lanes so

that they have identical values of X.19 Therefore both lane groups have the same delay, given by

(A.6). The control delay in equation (3), then, is just d multiplied by the number of signals.

Because we assume that all the lanes carrying through traffic equalize their volume-capacity

ratios, we can substitute our overall volume-capacity ratio V/VK for X, with capacity VK defined

appropriately as we now describe.

The arterial’s capacity is based on the saturation flow rates, si, of the two lane groups,

along with the fraction of time the signal is green and the proportion of traffic at each

intersection that is making left turns. (This latter proportion gets to use the left-turn lane,

assumed to have ample capacity, so can be added to the capacity of the other two lane groups.)

Saturation flow means the highest flow rate that can pass through the intersection while the light

is green. Based on equation 16-6 of the HCM and using i to index lane groups, the capacity of

each lane group (denoted in the HCM by ci) is:

)/( Cgsc iii ⋅= (A.7)

where the effective green ratio gi/C is here taken to be identical for both the through group and

shared right-turn/through group, hence g/C.

Adding the fraction τLT of traffic volume that is making left turns, the total capacity of the

road — VK in our model — is:

19 It is also assumed that vehicles are not allowed to turn right during red signal phases.

31

)()1( 1RTTLTK ccV +−= −τ (A.8)

where cT and cRT are the capacities of the through and right-turn lane groups. We assume that

7.5% of the total traffic volume will be vehicles turning left, and similarly for vehicles turning

right, so τLT = τRT = 0.075.20

The saturation flow rates needed for (A.7) are given by equation 16-4 of the HCM, which

includes various adjustment factors. Many of these are equal to one because we use the

corresponding HCM recommended default values (see Chapters 10 and 16). Specifically, we

assume that the road is located in a non-CBD area and on level terrain, no parking is allowed,

there are no buses that stop within the intersection area, and no adjustments are necessary for

pedestrians or bicycles. Since we are interested in estimating capacity, we assume that there is

uniform use of the available lanes (i.e., there is no adjustment for lane utilization), as

recommended by the HCM (p. 10-26). Also, there are no left-turn adjustments since we assume a

separate, exclusive left-turn lane and treat any delay in making left turns (which happens at most

once in any trip) as part of the access time to a final destination rather than delay time on the

road in question. We also follow the HPMS Field Manual’s lead and multiply the HCM’s

original equation for saturation flow by the peak hour factor (PHF) rather than adjusting volumes

by that factor (see p. N-19 of the HPMS Field Manual).

With these assumptions, the saturation flow rate for a lane group is:

PHFffNfss RTHVw0=

where s0 is the base saturation flow rate per lane (pce/h/ln), N is the number of lanes in the lane

group, fw is the adjustment factor for lane width, fHV is the adjustment factor for heavy vehicles,

and fRT is the adjustment factor (applying only to the right-turn group and accounting for vehicles

having to reduce speed to make the turn). The HCM recommends s0 = 1,900 pce/h/ln. The lane

width adjustment, fLW, is 1 when lane width is 12 ft and 0.93 when lane width is 10 ft. Assuming

the percentage of heavy vehicles in the traffic stream is 5% as in the case of expressways, fHV =

0.95 (different from the heavy vehicle adjustment factor for expressways). For the shared right-

turn/through lane group, the right-turn adjustment factor fRT is 1-0.15PRT, where PRT is the 20 A typical urban trip length is 10 miles (Pisarski, 2006). Using Lake Shore Drive in Chicago as an example road, there are 1.5 exits per mile, or 7.5 exits passed by a typical trip if half of it takes place on the arterial. We assume therefore that a fraction 1/7.5 = 0.133 of trips exit at each exit. We raise this to 0.15 to account for the likelihood that the critical bottleneck intersections are those with the most turning traffic. If left and right turns are evenly balanced, that gives 7.5% right turns and 7.5% left turns at the intersection whose capacity is being computed.

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percentage of right-turning vehicles in that lane group. As mentioned earlier, the proportion of

total traffic volume that turns right at each intersection is τRT = 0.075. This gives us PRT equal to

0.152 and 0.230, and correspondingly, fRT equal to 0.978 and 0.966, for the two-lane and three-

lane arterials in our example.21 For the through lane group, fRT = 1 by definition. As in the case of

expressways, the peak hour factor, PHF, is assumed to be 0.92.

21 Let the saturation flow rate of the through lane and the number of through lanes of a particular arterial be denoted by sT and n, respectively. The saturation flow rate for the right-turn lane group is sRT = sT(1 – 0.15PRT). At capacity, PRT is the number of vehicles turning right divided by the capacity of the right-turning lane group: τRT[nsT + sT(1 – 0.15PRT)]/[sT(1 – 0.15PRT)]. After simplifying, we obtain a quadratic equation in terms of PRT, which can be solved for a value of PRT between 0 and 1 for given n and τRT.

33

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